[ 26 9 ] 
“ advanced to him in confidcration of fuch fecurity, 
<c reckoning compound intereft at four per cent. 
M. de Moivre’s directions, in his treatife on an- 
nuities, prob. XVII. and XX. lead us to feek the re- 
quired fum in this cafe, by the following procefs. 
Find firft, the prefent fum A fhould receive for the 
reverfion of 40/. per mm. for ever after his death, 
fuppofing it not dependent on his furviving B. — The 
prefent value of fuch a reverfion, is the value of 
the life fubtraCted from the perpetuity *. The 
value of the life, taken from Mr. de Moivre’s tables, 
is 13.2 years purchafe. This fubtraCted from 25, 
the perpetuity, leaves 11.8, the value of the fup- 
pcfed eflate after the life of A ; which value there- 
fore, is in money 472 /. But (as M. de Moivre 
cbferves), the lender having a chance to lofe his 
money, a compenfation ought to be made to him 
for the rifk he runs, which is founded on the pofiibi- 
lity that a man of the age of40 may not furvive another 
perfon of the fame age. This chance is an equal 
chance j and therefore half the preceding fum, or 
236/. is the fum which fhould be advanced now on 
the expectation mentioned. 
This folution carries a plaufible appearance ; and 
moft perfons will, probably, be ready to pronounce 
it right ; nor will this be any wonder, as fo great a 
mafter of thefe fubjeCts as M. de Moivre, appears to 
have been mifled by it. Nothing more is necefiary 
to prove it to be fallacious, than proceeding in the 
fame way to folve the following fimilar queition. 
“ A, aged 40, offers to give fecurity for 40/. per 
<c ann. to be entered upon at his death, provided it 
* By Prob. XXVI. p. 293, of Mr, Simpfon’s ScleCt Exercifes. 
“ fhould 
a. - 
